Problem: What do the following two equations represent? $-5x+4y = -1$ $5x-4y = 5$
Solution: Putting the first equation in $y = mx + b$ form gives: $-5x+4y = -1$ $4y = 5x-1$ $y = \dfrac{5}{4}x - \dfrac{1}{4}$ Putting the second equation in $y = mx + b$ form gives: $5x-4y = 5$ $-4y = -5x+5$ $y = \dfrac{5}{4}x - \dfrac{5}{4}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.